1. Field of the Invention
This invention is related in general to the field of vertical-scanning interferometry and, in particular, to a novel approach for deriving surface-profile measurements from irradiance modulation signals.
2. Description of the Related Art
Vertical scanning interferometry (VSI) is a technique where broad bandwidth light, such as white light, is used as a light source in an interferometer and the degree of modulation, or coherence, of interference fringes produced by the instrument is measured for various distances between a test surface and the reference surface of the interferometer (each corresponding to a different optical path difference, OPD) to determine surface height. The method typically involves vertical scanning of the reference arm of the interferometer with respect to a stationary sample and calculation of the relative modulation of the intensity signal as a function of vertical position.
As illustrated in simple schematic form in FIG. 1 and described in further detail in U.S. Pat. No. 4,340,306 and U.S. Pat. No. 5,204,734, herein incorporated by reference, typical vertical scanning interferometric equipment 10 comprises a light source 12 directing a beam L of light through an illuminator 14 toward a beam splitter 16, which reflects the light downward in the direction of a test surface S. The light reflected by the beam splitter 16 passes through a microscope objective 22 focused on the test surface S. The objective incorporates an interferometer 23, such as Mirau, comprising a beam splitter 24 and a reference mirror 26 adapted for relative movement with respect to the test surface, so that two light beams are generated for producing interference fringes. The beams reflected from the reference mirror 26 and the test surface S pass back up through the optics of the microscope objective 22 and upward through the beam splitter 16 to a solid-state detector array 28 in a camera 30 in coaxial alignment with the objective 22, so that two light beams produce interference fringes as a result of the optical path difference between the reference mirror and the test surface S. The imaging array 28 normally consists of individual charge-coupled-device (CCD) cells or other sensing apparatus adapted to detect and record a two-dimensional array of signals corresponding to interference effects produced by the interferometer as a result of light reflected at individual x-y-coordinate pixels in the surface S and received at corresponding individual cells in the array. Appropriate electronic hardware is provided to process the signals generated by each cell and transmit digitized light-intensity data D to a microprocessor for processing. The microscope objective 22, as well as the interferometer typically incorporated within it, is adapted for vertical movement (along the z coordinate) to focus the image of the test surface on the detector array 28. Thus, an interference-fringe map is generated by detecting the intensity of the light signal received in each cell of the array 28.
In vertical scanning interferometry, a profile of the surface S is produced by repeating irradiance measurement at different, normally constant-interval OPD's between the objective 22 and the test surface S (that is, at different elevations of the scanning mechanism), so as to provide information concerning the variation of light intensity at each pixel as the corresponding optical path difference is varied systematically with respect to an initial reference point. Thus, the position of the scanning mechanism corresponding to maximum interference at each pixel is determined and used, based on the distance from the reference point, to calculate the height of the surface at that pixel. Either the objective 22 or the test surface S is moved vertically to produce these repeated measurements (vertical scanning). It is noted that the present description is based on the configuration of a Mirau interferometer but, as one skilled in the art would readily understand, it is equally applicable to any of the other instruments used in vertical scanning interferometry, such as Michelson, Linnik or Fizeau.
The prior art discloses various ways by which VSI may be implemented to determine surface height by calculating the degree of fringe modulation, or coherence, of the interference fringes produced at the light detector for various OPD's between the test surface and the reference surface of the interferometer. All methods involve vertical scanning of the reference arm of the interferometer with respect to a stationary sample, or viceversa, and estimation of the vertical position corresponding to the peak of the modulation envelope from the intensity measurements collected during scanning.
When white light or broad-bandwidth light is used as the source of illumination in an interference microscope, the visibility of the fringes drops off rapidly from its maximum value at minimum OPD. FIG. 2 shows the modulation of a typical intensity signal I (irradiance) obtained from a detector cell in the image plane of the interferometer as the OPD is varied by vertically scanning the reference mirror (or the sample). A measurement of relative surface height at the vertical-scanning point corresponding to the fringe-visibility peak (also maximum fringe contrast) can thus be made. By simultaneously carrying out the procedure in parallel for each detector cell during vertical scanning, a three-dimensional height map can be obtained for the surface of the test sample.
In order to estimate the point of maximum fringe visibility from irradiance data, the amplitude-modulated carrier signal of FIG. 2 is demodulated and the scanning position corresponding to the modulation peak is calculated using one of several techniques. The detector array receives an amplitude-modulated input signal for the light intensity I, as illustrated in FIG. 2, which is given by: EQU I(z)=I.sub.o +m(z)cos(.omega..sub.o z+.alpha.), (1)
where I(z) is the light intensity at the detector, I.sub.o is the constant bias component of the signal (also known as the DC component), m(z) is the modulating signal, .omega..sub.o is the fringe signal, and .alpha. is the initial phase, which is assumed constant with respect to the vertical dimension z (the scanning coordinate producing a variable OPD).
It is known that the modulation signal m(z) approximates a bell-shaped function of the type illustrated in FIG. 3; therefore, the peak of the function m(z) corresponds to the maximum fringe visibility produced by the interferometer and to the scanning position z which is the target of the measurement. Note that the curve illustrated in FIG. 3 also corresponds to the upper envelope of the irradiance function of FIG. 2, shown in dotted line in that figure.
The peak of the modulation curve m(z) cannot be determined directly from the modulated carrier signals because these are not individually-measurable quantities and are not readily available from irradiance information. Therefore, all prior-art procedures utilize some form of the relationship of Equation 1 to estimate the peak of the modulation function m(z) from VSI light-intensity measurements and generate a corresponding height for the surface of the test sample S.
Several approaches have been developed for white-light scanning interferometry. For instance, see Caber, P. et al., "A New Interferometric Profiler for Smooth and Rough Surfaces," Proc. SPIE, Vol. 2088, 195-203, 1993; Kino, Gordon S. et al., "Mirau Correlation Microscope," Applied Optics, 29(26): 3775-3783, 1990; de Groot, Peter and L. Deck, "Three-Dimensional Imaging by Sub-Nyquist Sampling of White-Light Interferograms," Optics Letters, 18(17): 1462-1464, 1993; Danielson, Bruce L. et al., "Absolute Optical Ranging Using Low Coherence Interferometry," Applied Optics, 30(21): 2975-2979, 1991; Dresel, Thomas et al., "Three-Dimensional Sensing of Rough Surfaces by Coherence Radar," Applied Optics, 31(7): 919-925, 1992; and Davidson, Mark et al., "First Results of a Product Utilizing Coherence Probe Imaging for Wafer Inspection," SPIE Vol. 921, 100-114, 1988.
All of these publications describe elaborate approaches for determining the peak of the modulation function m(z) (Equation 1) from irradiance data I(z), deriving surface topography information from extensive processing of light intensity signals based on a determination of the OPD corresponding to the peak of the modulation curve illustrated in FIG. 3. In essence, they all strive to find the z value corresponding to the peak of m(z) by estimating the shape of the modulation envelope itself through a sequence of elaborate transformations and calculations. These processing steps require substantial electronic hardware dedicated to processing the light intensity signals produced by the interferometer in order to generate on-line height data corresponding to the peak of the modulation function envelope. Alternatively, in order to reduce hardware requirements and manufacturing costs, prior art apparatus and methods have also taken the approach of storing the irradiance signals in a memory on-line during scanning and subsequently processing the stored information by means of computer software. A typical computer-processing time for estimating the peak of the modulation function m(z) and for calculating the corresponding z utilizing these prior-art procedures is in the order of 10 seconds. Thus, the software approach reduces hardware costs but introduces a material delay in the availability of profiling results, which is very undesirable for on-line applications, such a when VSI is used for manufacturing quality control. Therefore, any faster and less hardware-dependent technique for determining height data from irradiance measurements would represent a valuable improvement in the art.
All prior-art techniques suffer from another drawback. In practice, depending on the roughness characteristics of the test surface and the scanning conditions, the modulation function m(z) is not always uniformly bell-shaped; rather, it usually exhibits multiple maxima that hinder a repetitive estimation of the peak corresponding to maximum fringe visibility. FIG. 4 is an illustration of such a modulation curve. In such cases it is difficult to distinguish one peak from another and no prior-art procedure provides an effective method for consistently selecting the same peak as the point corresponding to maximum fringe visibility. Therefore, inconsistent results are often obtained from rough interpixel surfaces. Similar modulation curves and results are also seen from inertial overshooting produced by very rapid motion during scanning.
As those skilled in the art readily understand, for the purpose of producing height data from VSI procedures it is not absolutely necessary to locate exactly the true peak of the modulation curve m(z), so long as the measured value of z is close to the z corresponding to the peak and its value can be obtained repetitively during a scanning operation. Therefore, the problem with the inability of prior-art procedures to consistently select the same peak when dealing with multi-maxima modulation curves lies in its lack of repeatability (or consistence of results), rather than in the actual deviation from the correct z value. Since vertical scanning produces relative positions, z values corresponding to off-peak modulations are acceptable so long as consistently repeatable. Therefore, any VSI technique that improved the repeatability of modulation-peak estimation would also be a very desirable improvement over the prior art.
This shortcoming of prior-art techniques in dealing with multi-peak modulation envelopes is particularly evident in measuring topographies with sharp, large steps occurring within a single pixel or a small number of adjacent pixels. When such profiles are scanned, the resulting irradiance signals tend to produce modulation envelopes with two distinct maxima (of the type shown in FIG. 4). This effect is believed to result from the high level of light scattering associated with sharp changes of elevation in the surface profile. In these situations, prior-art techniques seeking to determine a maximum point on the modulation envelope are inherently subjected to ambiguities that produce artifacts. This is particularly a problem in applications that require the ability to accurately measure sharp steps in the profile of a surface. It is noted, though, that the problem is not unique to the measurement of sharp steps, but it occurs whenever a surface contains significant interpixel variations, such as in the order of 10 nanometers or greater. This invention is directed at providing an approach that also improves prior-art techniques with respect to these problems.